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katiebugg

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\[\log _{3}27\]

cwrw238

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this means 3 ^x = 27
x = value of the log

katiebugg

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?

katiebugg

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x=3?

cwrw238

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3 ^ 3 = 27 right?

cwrw238

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yes

katiebugg

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ok :)

cwrw238

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the definition of a log is the exponent whci takes the base to the given number

katiebugg

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wait then whats \[\log _{2} 32\]

cwrw238

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eg 10^2 = 100
so log (10) of 100 = 2

cwrw238

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what power must 2 be taken to in order to get 32s

cwrw238

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* 32?

katiebugg

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umm 5?

cwrw238

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right

cwrw238

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are you getting the idea?

katiebugg

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kinnda lol i think what would \[\log _{3} 18 \] bee cuz i cant get it

cwrw238

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here 2 ^x = 18 where x = required log
now this cant solved by inspection as the other 2 could
so you preceed as follows:
ln 2^x = ln 18 where ln is natural log or log to base e
by laws of logs
x ln 2 = ln 18
x = ln 18 / ln 2
which you can do with your calculator

katiebugg

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its 3 tho

cwrw238

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oh - r us sure its log2 18 not log2 8?

cwrw238

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because 2^3 = 8

katiebugg

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nope log3 18

cwrw238

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log to base 3 of 18

katiebugg

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k

cwrw238

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gotta go katie